Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7190)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-2/3, b>=a

For fixed z and a=-2/3, b=14/3

http://functions.wolfram.com/07.23.03.7190.01

Input Form

Hypergeometric2F1[-(2/3), 14/3, -(9/2), -z] == (1/(419904 (1 + z)^(17/2))) ((419904 + 3302208 z + 11013120 z^2 + 19534592 z^3 + 17150848 z^4 - 4954752 z^5 - 6729501 z^6 - 4021826 z^7 - 1248072 z^8 - 162656 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (139968 + 1002240 z + 2976512 z^2 + 4488704 z^3 + 2752640 z^4 + 5135785 z^5 + 3458786 z^6 + 1166744 z^7 + 162656 z^8) Sinh[ArcSinh[Sqrt[z]]/3])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]